Equations
Add the complex numbers: (2 + 4i) + (5 + 6i)
7 + 10i
Does this parabola have a maximum or a minimum if the vertex is at (- 1, - 16) and the x-intercepts are at (- 5,0) & (3,0).
Minimum
Draw a graph with 2 real solutions.
Has to cross x-axis twice!
The highest or lowest point on the graph, where the curve makes its sharpest turn is called the...
Vertex OR Minimum/Maximum
What two methods can I always use to solve quadratic equations? Factoring, Quadratic Formula, Square Roots, Completing the Square.
Quadratic Formula & Completing the Square
Subtract the complex numbers: (6 + 7i) - (2 + 4i)
4 + 3i
What are the x-intercept(s) of the parabola y = (x + 6)(x - 2).
x = - 6. x = 2.
Draw a graph with 2 imaginary solutions.
Graph does not touch x-axis.
The point that is the same distance from the vertex as the vertex is to the directrix is called...
Focus
Solve x^2 + 5x + 4 by graphing, factoring, completing the square, square roots, or using the quadratic formula.
x = - 1, x = - 4
Multiply the complex numbers (2 + 3i)(4 + 5i)
-7 + 22i
What is the a, h, and k value and the vertex of this graph and equation? y = 2(x + 1)^2 - 4
a= 2, h= - 1, k= - 4
Draw a graph with 1 real solution.
Touches the x-axis once.
The line that is the same distance from the vertex as the vertex is to the focus is called the...
Directrix
Solve (x + 1)^2 = 16 by graphing, factoring, completing the square, square roots, or using the quadratic formula.
x = - 5, x = 3
Write the equation of the parabola using the following formula: y - k = - 1/(4p) (x - h)^2 when the vertex is at (-3,5) and focus is at (-3, 3).
y - 5 = - 1/8 (x + 3)^2
What is the domain in interval notation of the parabola y = (x + 9)(x + 7)?
(- infinity, infinity)
Write the solution to the quadratic inequality in interval notation if only the "U" part if shaded and the parabola and dashed line cross at (- 2, 5) and (3, 5).
(- 2, 3)
The line that divides a figure or function into two equal, mirror-image halves is called the...
(When an object is folded along this line, both sides match exactly)
Axis of symmetry
Solve x^2 + 6x - 7 by completing the square or using the quadratic formula.
x = - 7, x = 1
What is the quadratic equation in vertex or factored form when given three points- Vertex:(2,9), x-intercepts:(-1,0), (5,0).
Vertex: y= - (x - 2)^2 + 9
Factored: y = - (x - 5)(x + 1)
What is the range in interval notation of the parabola y = (x - 2)(x - 8) with a vertex at (- 5, - 9)?
[-9, infinity)
Juno throws a ball to see how long it takes to hit the ground. This is modeled by the equation y= (x + 5)(x - 2). The two solutions in seconds are x = -5 and x = 2. Identify which solution is extraneous and explain why.
x = - 5 is extraneous because it is negative, cannot be negative in this real world scenario. (not a possible real value- cant go back in time)
The distance between the focus and vertex is represented by...
p
Solve x^2 + x +1 by using the quadratic formula.
(-1 +/- (sqrt(3))i) / 2